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Shinji Machida KEK FFAG Workshop 2002, February 13-15

Basic Design of Optics in FFAG 1. Essential functions of FFAG 2. Linearized calculation -singlet (FODO) -triplet -two beam accelerator. Shinji Machida KEK FFAG Workshop 2002, February 13-15. First impression of (scaling) FFAG. FFAG looks like a cyclotron.

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Shinji Machida KEK FFAG Workshop 2002, February 13-15

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  1. Basic Design of Optics in FFAG1. Essential functions of FFAG2. Linearized calculation-singlet (FODO) -triplet -two beam accelerator Shinji Machida KEK FFAG Workshop 2002, February 13-15

  2. First impression of (scaling) FFAG • FFAG looks like a cyclotron. • Magnetic field has a complicated shape. • Even closed orbit cannot be calculated by hand because the ideal orbit is not on the constant bending field. Much more complicated optics than synchrotron and cyclotron.

  3. Essence of focusing structure • Body of a normal bend has focusing action. • Body of a reverse bend has defocusing action. • The lowest order of those is quadrupole like. • Both has defocusing edge.

  4. Simplified closed orbit • In magnets, orbit draws arcs with almost constant curvature. • Total bending angle per cell is 2p/N. • Ratio of bend angles in F and D is (BL)F/(BL)D.

  5. Singlet (FODO) When qF, bF, and bD are given, then the orbit is determined With k-value, the optics (focusing) is also determined. However, it is not clear if the optics is stable.

  6. Model a magnet as a combined function type. Edge focusing and fringe field is included as a synchrotron magnet. /* SAD INPUT EXAMPLE*/ BEND BFN=(L=1.0 ANGLE=58 DEG K1 =3.663E1=0.934 E2=0.934) BDN=(L=1.0 ANGLE=13 DEG K1=-2.092E1=1.114 E2=1.114) ; DRIFT LDR=(L=0.1410) ; LINE CELL=(BFN LDR BDN LDR) ; Quick way to obtain lattice parameters

  7. Example: singlet 8 cell • # of cell 8 • Bend angle 58 at F -13 at D • Phase advance per cell 100 deg. for H 57 deg. for V

  8. Triplet In the same way as singlet, Triplet has longer straight.

  9. Example: triplet 8 cell • # of cell 8 • Bend angle 58 deg. at F -13 deg. at D • Phase advance per cell 95 deg. for H 57 deg. for V

  10. Two Beam Accelerator In addition to the singlet conditions, and assume

  11. Example: two beam acc. 16 cell • # of cell 16 • Bend angle 52 deg. at F -30 deg. at D • Phase advance per cell 124 deg. for H 156 deg. for V

  12. Summary • Although the orbit and optics of FFAG in reality are complicated, a linearized model with constant curvature and constant quadrupole focusing strength gives pretty good approximation to initiate lattice design. (It was confirmed by the comparison with a brute force tracking using field mapping data.) • Practical procedures to design singlet (FODO), triplet, and two beam accelerator lattice are given. • The next step is to take into account higher order effects semi-analytically.

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